Cardiovascular diseases are common and life-threatening, making them the prime killer in the United States. Magnetic resonance imaging (MRI) is considered a very promising candidate for clinical cardiac imaging, due in part to its safety, its image contrast and its flexibility in the positioning of imaging planes/volumes. The present work aims at improving the diagnostic value of cardiac MRI exams, with the understanding that an accurate diagnosis may lead to successful treatment and monitoring. A great challenge for MRI in cardiac applications comes from the need to freeze or resolve both cardiac and respiratory motions. Suppressing the respiratory motion through breath-holding is not an option for longer, more elaborate studies. Although respiratory-compensated, free-breathing cardiac imaging has been shown to provide useful clinical information, further performance improvements are believed to be limited chiefly by residual respiratory blurring/artifacts. The novel approach at respiratory-compensation introduced here is expected to detect and correct respiratory motion much more accurately/completely than existing strategies, hopefully increasing spatial resolution through a reduction in blurring. Very fast 3D imaging will be developed to resolve the respiratory cycle. Respiration-monitoring stretchable belts, a standard product available with essentially any MRI scanner, provide a very high temporal resolution account of how respiration proceeds during a scan. The wealth of spatial/geometrical information provided by our fast 3D imaging sequence will be fused with the very high temporal resolution information from a respiration-monitoring belt, to detect and correct for the spatially and temporally complex respiration-induced motion and deformation of the heart. Once the data will be corrected for the effect of respiration, it will be converted from a time series of images (where respiratory motion can be detected and corrected) to a cardiac-phase series of images (where the cardiac beating motion can be seen). As a result, a respiratory-compensated cardiac-phase series of 3D images of the heart will be generated. This approach has the potential of being especially useful in patients for whom breath-holding is not an option, e.g. when imaging very sick, mentally impaired or infant patients.